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Random Variables and Probability Distributions 41

F X (x)

1

1
2

1
8
x
–2 –1 0 1 2 3

Figure 3.1 Probability distribution function of X, F X 9x), for Example 3.1

F X (x)

1.0

0.2
x
–1 0 1
Figure 3.2 Probability distribution function of a continuous random variable X, F X 9x)

3.2.2 PROBABILITY MASS FUNCTION FOR DISCRETE RANDOM
VARIABLES

Let X be a discrete random variable that assumes at most a countably infinite
number of values x , x 2 ,... with nonzero probabilities. If we denote
1
P9X ˆ x i ) ˆ p9x i ), i ˆ 1, 2, . . ., then, clearly,
9
0 < p x i † 1; for all i; =
X 3:4†
p x i †ˆ 1:
;
i

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